Holomorphically projective mappings of special Kähler manifolds

Kiosak, V.; Savchenko, A. M.; Shevchenko, T. I.

doi:10.1063/1.5064924

Cited by 28 publications

(10 citation statements)

References 7 publications

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“…The developed methods can be applied for study of holomorphic-projective mappings of Kählerian spaces and other mappings of generalized spaces, [12,17]. The obtained results can find an application in the general relativity theory and mechanics, [3].…”

Section: Discussionmentioning

confidence: 94%

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

Кіосак¹,

Пришляк

Lesechko

2021

PIGC

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В роботі досліджуються два псевдоріманових простори, які мають спільні геодезичні лінії. Вимагається виконання умов алгебраїчного та диференціального характеру на тензор Рімана одного з них. А операція опускання індексів та обчислення коваріантної похідної здійснюється відносно метрики та об'єктів зв'язності іншого простору. Для досліджень використовується спеціальний допоміжний тензор. Доведено, що виконання додаткових умов приводить до просторів, що не допускають нетривіальних геодезичних відображень, або простори належать до еквідістантних просторів. Використовуються тензорні методи без обмежень на знак метрики.

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Section: Discussionmentioning

confidence: 94%

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

Кіосак¹,

Пришляк

Lesechko

2021

PIGC

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“…It is demonstrated that conformally flat conformal reducible pseudo-Riemannian spaces are quasi-Einstein spaces. Results of the paper can be effectively applied for further research in mechanics, geometry, general relativity theory [17,27] and topology [20]. In particular, under certain conditions, the obtained equations describe the state of an ideal fluid.…”

Section: Discussionmentioning

confidence: 94%

On conformally reducible pseudo-Riemannian spaces

Shevchenko

Спічак

Дойков

2021

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The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.

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“…A Kähler space K n , (n = 2N ), is a pseudo-Riemannian space with a metric tensor g ij (x) containing structure F h i (x), which satisfies the following condition, [3,6,19]:…”

Section: Generalized φ(Ric)-vector Fields In Kählerian Spacesmentioning

confidence: 99%

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

Vashpanova¹,

Savchenko²,

Vasylieva³

2021

PIGC

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The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.

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Holomorphically projective mappings of special Kähler manifolds

Cited by 28 publications

References 7 publications

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

On conformally reducible pseudo-Riemannian spaces

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

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